# Dimensional Analysis :<

1. May 13, 2009

### yuukichi

Hi guys, have been reading these forums for a very long time, have always found it very helpful and informative.

There's this problem which I cant seem to get my head around, it seems very straight forward, but every time I try to do it, I always end up doing it wrong. I would greatly appreciate it if anyone could point me in the right direction.

The problem is:

Dimensional analysis showed that the following relation describes the drag force F on an airplane

$$\frac{F}{\rho d^{2}u^{2}}$$ = f$$\left(\frac{\mu}{\rho l u}\right)$$

Where u the airplane velocity, l is the characteristic length of the airplane, $$\rho$$ is the surrounding air density and $$\mu$$ is the viscosity of the air.
The drag on an airplane cruising at 390km/h in air at atmospheric pressure and temperature is to be determined from tests on a 1:10 scale model placed in a pressurised wind tunnel. To minimise compressibility effect the air speed in the wind tunnel is also to be 390km/h. Determine the air pressure in the wind tunnel, assuming the air temperature for the model and prototype.

I've tried separating F on the LHS by introducing a constant in the RHS, but that ends up totally wrong

Any help would be greatly appreciated!

Thanks :)

2. Jun 8, 2009

### Lojzek

The only unknown thing is the function f: one must measure it experimentaly. If you only care about one particular real life problem, then you only need the value of f for that problem: you get this value by one experiment on the model that gives the same argument for f as the real life problem.

3. Feb 19, 2010

### ivraj

hey thread what answer did u get fir this question. pliz help me everyone.

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